Equatorial and related non-equilibrium states in magnetization dynamics of ferromagnets: Generalization of Suhl's spin-wave instabilities

We investigate the nonlinear dynamics underlying the evolution of a 2-D nanoscale ferromagnetic film with uniaxial anisotropy in the presence of perpendicular pumping. Considering the associated Landau-Lifshitz spin evolution equation with Gilbert damping together with Maxwell equation for the demagnetization field, we study the dynamics in terms of the stereographic variable. We identify several new fixed points for suitable choice of external field in a rotating frame of reference. In particular, we identify explicit equatorial and related fixed points of the spin vector in the plane transverse to the anisotropy axis when the pumping frequency coincides with the amplitude of the static parallel field. We then study the linear stability of these novel fixed points under homogeneous and spin wave perturbations and obtain a generalized Suhl's instability criterion, giving the condition for exponential growth of P-modes under spin wave perturbations. Two parameter phase diagrams (in terms of amplitudes of static parallel and oscillatory perpendicular magnetic fields) for stability are obtained, which differ qualitatively from those for the conventional ferromagnetic resonance near thermal equilibrium and are amenable to experimental tests.